Western Electric
Run rules on the sigma zones, not just the 3σ line.
A point beyond 3 sigma is not the only signal a control chart gives. The Western Electric rules read patterns in the sigma zones, runs, trends, clustering, so a process change is caught before any single point ever breaches a limit.
What it measures
The rules divide each half of the control chart into three zones by standard deviation, zone A (2 to 3 sigma), zone B (1 to 2 sigma), zone C (0 to 1 sigma), and watch for patterns too unlikely to be chance:
- Rule 1: one point beyond 3 sigma (zone A's outer edge). The classic single-point alarm.
- Rule 2: two of three consecutive points in zone A or beyond, on one side. A shift the single-point rule would miss.
- Rule 3: four of five consecutive points in zone B or beyond, on one side. A sustained smaller shift.
- Rule 4: eight (or nine) consecutive points on one side of the centerline. A process that has quietly moved off center.
Each pattern has a low probability of occurring by chance in a stable process, so its appearance is evidence of a special cause, a real change, well before the process wanders far enough for one point to cross the 3 sigma line.
How to read the output
The rules trade a little false-alarm rate for much earlier detection. A run of points all on one side, or creeping into zone B and A, says the process has shifted even though nothing has breached yet, and that early warning is the whole value. The tuning question is how many rules to run: more rules catch more real shifts but raise the false-alarm rate, so a noisy, low-stakes parameter might use only Rule 1 and Rule 4, while a critical characteristic justifies the full set. The pattern, not the single dramatic point, is what these rules are built to surface.
A real use case
A formation step charts discharge capacity per build. No point ever breaches the control limits, so a basic chart shows nothing, but the run rules fire: eight consecutive builds land just below the centerline, then four of five drop into zone B. Capacity has shifted down by a fraction of a sigma, invisible as any single point but unmistakable as a pattern. The rule flags it, and the investigation traces the drift to a slowly aging reference electrode in the formation rig before the shift grows large enough to push cells out of spec. The process change was caught by its pattern, days before a single-point alarm would have seen it.
Common mistakes
- Running only Rule 1. Limiting the chart to single-point breaches throws away most of its early-warning power.
- Turning on every rule everywhere. More rules raise the false-alarm rate; match the rule set to how critical and how noisy the characteristic is.
- Applying run rules to an unstable spread. The zones are defined from sigma; if the range chart is not in control, the zones move and the patterns mislead.
- Treating a run-rule signal as a different, lesser alarm. A pattern is a special cause just as much as a breach, and deserves an investigation.
- Hunting patterns by eye instead of applying the rules consistently, which finds shapes that are not really there and misses ones that are.
Pattern detection on the zones, not just the 3 sigma line
Niobia applies the Western Electric run rules to the control charts it builds, scoring every new point against the zone patterns, two of three in zone A, four of five in zone B, eight on one side, so a sustained or creeping shift is flagged before any single point breaches. It runs together with the X-bar and R charts and the EWMA view, giving three complementary lenses on a drift: the single-point breach, the zone pattern, and the accumulated average. A confirmed pattern becomes an excursion alertto the right engineer with the rule that fired.
Frequently asked
Why use run rules if I already have control limits?
Because most process shifts are too small to push a single point past 3 sigma, but they leave a pattern: a run on one side, a creep into the outer zones. The run rules detect those patterns, catching real changes days or shifts before a single-point breach would.
Don't more rules just mean more false alarms?
They raise the false-alarm rate, yes, which is why the rule set should match the characteristic. A critical, well-resolved parameter justifies the full set; a noisy, low-stakes one might use only the single-point and one-sided-run rules. It is a sensitivity-versus-noise trade-off.
Are Western Electric and Nelson rules the same thing?
They are closely related zone-based run-rule sets, with slightly different specifics (Nelson adds a few patterns like alternating points and stratification). Both formalize the same idea: non-random patterns in the zones signal a special cause before a 3-sigma breach.